Standart rasterization covers all texels where just the texel center is inside the triangle, that includes only partially covered texels at the edges.

It would be possible to skip those texels with exact edge tests in PS or probably better with vertex adjustments in GS.

But a 'fully covered only' mode for conservative rasterization would be best. I assumed this is already possible,

but after a quick search it seems that's not the case: https://developer.nvidia.com/content/dont-be-conservative-conservative-rasterization